Generative Adversarial Networks (GAN)

By Prof. Seungchul Lee
http://iai.postech.ac.kr/
Industrial AI Lab at POSTECH

Table of Contents

Source

• 1시간만에 GAN(Generative Adversarial Network) 완전 정복하기
  • by 최윤제 (고려대 석사생)
  • YouTube: https://www.youtube.com/watch?v=odpjk7_tGY0
  • Slides: https://www.slideshare.net/NaverEngineering/1-gangenerative-adversarial-network

• CSC321 Lecture 19: GAN
  • By Prof. Roger Grosse at Univ. of Toronto
  • http://www.cs.toronto.edu/~rgrosse/courses/csc321_2018/

• CS231n: CNN for Visual Recognition
  • Lecture 13: Generative Models
  • By Prof. Fei-Fei Li at Stanford University
  • http://cs231n.stanford.edu/

1. Discriminative Model v.s. Generative Model

• Discriminative model

• Cenerative model

2. Density Function Estimation

• Probability

• What if $x$ is actual images in the training data? At this point, $x$ can be represented as a (for example) $64\times 64 \times 3$ dimensional vector.
  • the following images are some realizations (samples) of $64\times 64 \times 3$ dimensional space

• Probability density function estimation problem

• If $P_{\text{model}}(x)$ can be estimated as close to $P_{\text{data}}(x)$, then data can be generated by sampling from $P_{\text{model}}(x)$.

  • Note: Kullback–Leibler Divergence is a kind of distance measure between two distributions

• Learn determinstic transformation via a neural network
  • Start by sampling the code vector $z$ from a simple, fixed distribution such as a uniform distribution or a standard Gaussian $\mathcal{N}(0,I)$
  • Then this code vector is passed as input to a deterministic generator network $G$, which produces an output sample $x=G(z)$
  • This is how a neural network plays in a generative model (as a nonlinear mapping to a target probability density function)

- An example of a generator network which encodes a univariate distribution with two different modes

• Generative model of high dimensional space

• Generative model of images
  • learn a function which maps independent, normally-distributed $z$ values to whatever latent variables might be needed to the model, and then map those latent variables to $x$ (as images)
  • first few layers to map the normally distributed $z$ to the latent values
  • then, use later layers to map those latent values to an image

3. Generative Adversarial Networks (GAN)

• In generative modeling, we'd like to train a network that models a distribution, such as a distribution over images.

• GANs do not work with any explicit density function !

• Instead, take game-theoretic approach

3.1. Adversarial Nets Framework

• One way to judge the quality of the model is to sample from it.

• Model to produce samples which are indistinguishable from the real data, as judged by a discriminator network whose job is to tell real from fake

• The idea behind Generative Adversarial Networks (GANs): train two different networks

• Discriminator network: try to distinguish between real and fake data

• Generator network: try to produce realistic-looking samples to fool the discriminator network

3.2. Objective Function of GAN

• Think about a logistic regression classifier (or cross entropy loss $(h(x),y)$)

$$\text{loss} = -y \log h(x) - (1-y) \log (1-h(x))$$

• To train the discriminator

• To train the generator

• Non-Saturating Game when the generator is trained

  • Early in learning, when $G$ is poor, $D$ can reject samples with high confidence because they are clearly different from the training data. In this case, $\log(1-D(G(z)))$ saturates.
    
    
  • Rather than training $G$ to minimize $\log(1-D(G(z)))$ we can train $G$ to maximize $\log D(G(z))$. This objective function provides much stronger gradients early in learning.

3.3. Soving a MinMax Problem

Step 1: Fix $G$ and perform a gradient step to

$$\max_{D} E_{x \sim p_{\text{data}}(x)}\left[\log D(x)\right] + E_{x \sim p_{z}(z)}\left[\log (1-D(G(z)))\right]$$

Step 2: Fix $D$ and perform a gradient step to

$$\max_{G} E_{x \sim p_{z}(z)}\left[\log D(G(z))\right]$$

OR

Step 1: Fix $G$ and perform a gradient step to

$$\min_{D} E_{x \sim p_{\text{data}}(x)}\left[-\log D(x)\right] + E_{x \sim p_{z}(z)}\left[-\log (1-D(G(z)))\right]$$

Step 2: Fix $D$ and perform a gradient step to

$$\min_{G} E_{x \sim p_{z}(z)}\left[-\log D(G(z))\right]$$

4. GAN with MNIST

4.1. GAN Implementation

import tensorflow as tf
import matplotlib.pyplot as plt
import numpy as np

from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets('MNIST_data/', one_hot=True)

Extracting MNIST_data/train-images-idx3-ubyte.gz
Extracting MNIST_data/train-labels-idx1-ubyte.gz
Extracting MNIST_data/t10k-images-idx3-ubyte.gz
Extracting MNIST_data/t10k-labels-idx1-ubyte.gz

n_D_input = 28*28
n_D_hidden = 256
n_D_output = 1

n_G_input = 100
n_G_hidden = 256
n_G_output = 28*28

weights = {
    'G1' : tf.Variable(tf.random_normal([n_G_input, n_G_hidden], stddev = 0.01)),
    'G2' : tf.Variable(tf.random_normal([n_G_hidden, n_G_output], stddev = 0.01)),
    'D1' : tf.Variable(tf.random_normal([n_D_input, n_D_hidden], stddev = 0.01)),
    'D2' : tf.Variable(tf.random_normal([n_D_hidden, n_D_output], stddev = 0.01))
}

biases = {
    'G1' : tf.Variable(tf.zeros([n_G_hidden])),
    'G2' : tf.Variable(tf.zeros([n_G_output])),
    'D1' : tf.Variable(tf.zeros([n_D_hidden])),
    'D2' : tf.Variable(tf.zeros([n_D_output]))
}

z = tf.placeholder(tf.float32, [None, n_G_input])
x = tf.placeholder(tf.float32, [None, n_D_input])

def generator(G_input, weights, biases):
    hidden = tf.nn.relu(tf.matmul(G_input, weights['G1']) + biases['G1'])
    output = tf.nn.sigmoid(tf.matmul(hidden, weights['G2']) + biases['G2'])
    return output

def discriminator(D_input, weights, biases):
    hidden = tf.nn.relu(tf.matmul(D_input, weights['D1']) + biases['D1'])
    output = tf.nn.sigmoid(tf.matmul(hidden, weights['D2']) + biases['D2'])
    return output

def make_noise(n_batch, n_G_input):
    return np.random.normal(size = (n_batch, n_G_input))

G_output = generator(z, weights, biases)

D_fake = discriminator(G_output, weights, biases)
D_real = discriminator(x, weights, biases)

Step 1: Fix $G$ and perform a gradient step to

$$\min_{D} E_{x \sim p_{\text{data}}(x)}\left[-\log D(x)\right] + E_{x \sim p_{z}(z)}\left[-\log (1-D(G(z)))\right]$$

Step 2: Fix $D$ and perform a gradient step to

$$\min_{G} E_{x \sim p_{z}(z)}\left[-\log D(G(z))\right]$$

D_loss = tf.reduce_mean(- tf.log(D_real) - tf.log(1 - D_fake))
G_loss = tf.reduce_mean(- tf.log(D_fake))

D_var_list = [weights['D1'], biases['D1'], weights['D2'], biases['D2']]
G_var_list = [weights['G1'], biases['G1'], weights['G2'], biases['G2']]

LR = 0.0002
D_optm = tf.train.AdamOptimizer(LR).minimize(D_loss, var_list = D_var_list)
G_optm = tf.train.AdamOptimizer(LR).minimize(G_loss, var_list = G_var_list)

n_batch = 100
n_iter = 50000
n_prt = 5000

sess = tf.Session()
sess.run(tf.global_variables_initializer())

D_loss_record = []
G_loss_record = []
for epoch in range(n_iter):
    train_x, train_y = mnist.train.next_batch(n_batch)
    noise = make_noise(n_batch, n_G_input)

    # discriminator and generator are separately trained 
    sess.run(D_optm, feed_dict = {x: train_x, z: noise})
    sess.run(G_optm, feed_dict = {z: noise}) 
    
    if epoch % n_prt == 0:
        D_loss_val = sess.run(D_loss, feed_dict = {x: train_x, z: noise})
        G_loss_val = sess.run(G_loss, feed_dict = {z: noise})
        D_loss_record.append(D_loss_val)
        G_loss_record.append(G_loss_val)
    
        print('Epoch:', '%04d' % epoch, 'D_loss: {:.4}'.format(D_loss_val), 'G_loss: {:.4}'.format(G_loss_val))
        
        plt.figure(figsize = (10,5))
        plt.subplot(1,2,1)
        noise = make_noise(n_batch, n_G_input)
        G_img = sess.run(G_output, feed_dict = {z: noise})   
        plt.imshow(G_img[0,:].reshape(28,28), 'gray')
        plt.axis('off')
        plt.subplot(1,2,2)
        noise = make_noise(n_batch, n_G_input)
        G_img = sess.run(G_output, feed_dict = {z: noise})   
        plt.imshow(G_img[0,:].reshape(28,28), 'gray')
        plt.axis('off')
        plt.show()

Epoch: 0000 D_loss: 1.357 G_loss: 0.7241

Epoch: 5000 D_loss: 0.3976 G_loss: 2.334

Epoch: 10000 D_loss: 0.3858 G_loss: 2.29

Epoch: 15000 D_loss: 0.4858 G_loss: 2.409

Epoch: 20000 D_loss: 0.4215 G_loss: 2.505

Epoch: 25000 D_loss: 0.6568 G_loss: 1.829

Epoch: 30000 D_loss: 0.7463 G_loss: 1.935

Epoch: 35000 D_loss: 0.6776 G_loss: 2.18

Epoch: 40000 D_loss: 0.7029 G_loss: 1.809

Epoch: 45000 D_loss: 0.8303 G_loss: 1.789

4.2. After Training

• After training, use the generator network to generate new data

noise = make_noise(n_batch, n_G_input)
G_img = sess.run(G_output, feed_dict = {z: noise})

plt.figure(figsize = (5,5))
plt.imshow(G_img[0,:].reshape(28,28), 'gray')
plt.axis('off')
plt.show()

5. Conditional GAN

• In an unconditioned generative model, there is no control on modes of the data being generated.

• In the Conditional GAN (CGAN), the generator learns to generate a fake sample with a specific condition or characteristics (such as a label associated with an image or more detailed tag) rather than a generic sample from unknown noise distribution.

• Simple modification to the original GAN framework that conditions the model on additional information for better multi-modal learning

• Many practical applications of GANs when we have explicit supervision available

import numpy as np
import matplotlib.pyplot as plt
import tensorflow as tf

from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("./mnist/data/", one_hot=True)

Extracting ./mnist/data/train-images-idx3-ubyte.gz
Extracting ./mnist/data/train-labels-idx1-ubyte.gz
Extracting ./mnist/data/t10k-images-idx3-ubyte.gz
Extracting ./mnist/data/t10k-labels-idx1-ubyte.gz

n_D_input = 28*28
n_D_hidden = 256
n_D_output = 1

n_G_input = 128
n_G_hidden = 256
n_G_output = 28*28

n_label = 10 # one-hot-encoding

weights = {
    'G1' : tf.Variable(tf.random_normal([n_G_input + n_label, n_G_hidden], stddev = 0.01)),
    'G2' : tf.Variable(tf.random_normal([n_G_hidden, n_G_output], stddev = 0.01)),
    'D1' : tf.Variable(tf.random_normal([n_D_input + n_label, n_D_hidden], stddev = 0.01)),
    'D2' : tf.Variable(tf.random_normal([n_D_hidden, n_D_output], stddev = 0.01))
}

biases = {   
    'G1' : tf.Variable(tf.zeros([n_G_hidden])),
    'G2' : tf.Variable(tf.zeros([n_G_output])),
    'D1' : tf.Variable(tf.zeros([n_D_hidden])),
    'D2' : tf.Variable(tf.zeros([n_D_output]))
}

z = tf.placeholder(tf.float32, [None, n_G_input])
x = tf.placeholder(tf.float32, [None, n_D_input])
c = tf.placeholder(tf.float32, [None, n_label])

def generator(G_input, label, weights, biases):
    hidden = tf.nn.relu(tf.matmul(tf.concat([G_input, label], 1), weights['G1']) + biases['G1'])    
    output = tf.nn.sigmoid(tf.matmul(hidden, weights['G2']) + biases['G2'])
    return output

def discriminator(D_input, label, weights, biases):
    hidden = tf.nn.relu(tf.matmul(tf.concat([D_input, label], 1), weights['D1']) + biases['D1'])
    output = tf.nn.sigmoid(tf.matmul(hidden, weights['D2']) + biases['D2'])
    return output

def make_noise(n_batch, n_G_input):
    return np.random.normal(size = (n_batch, n_G_input))

G_output = generator(z, c, weights, biases)
D_fake = discriminator(G_output, c, weights, biases)
D_real = discriminator(x, c, weights, biases)

D_loss = tf.reduce_mean(-tf.log(D_real)-tf.log(1 - D_fake))
G_loss = tf.reduce_mean(-tf.log(D_fake))

D_var_list = [weights['D1'], biases['D1'], weights['D2'], biases['D2']]
G_var_list = [weights['G1'], biases['G1'], weights['G2'], biases['G2']]

LR = 0.0002
D_optm = tf.train.AdamOptimizer(LR).minimize(D_loss, var_list = D_var_list)
G_optm = tf.train.AdamOptimizer(LR).minimize(G_loss, var_list = G_var_list)

n_batch = 100
n_iter = 50000
n_prt = 5000

sess = tf.Session()
sess.run(tf.global_variables_initializer())

D_loss_record = []
G_loss_record = []
for epoch in range(n_iter):
    train_x, train_y = mnist.train.next_batch(n_batch)
    noise = make_noise(n_batch, n_G_input)

    # discriminator and generator are separately trained 
    sess.run(D_optm, feed_dict = {x: train_x, z: noise, c: train_y})
    sess.run(G_optm, feed_dict = {z: noise, c: train_y})

    if epoch % n_prt == 0:
        D_loss_val = sess.run(D_loss, feed_dict = {x: train_x, z: noise, c: train_y})
        G_loss_val = sess.run(G_loss, feed_dict = {z: noise, c: train_y})
        D_loss_record.append(D_loss_val)
        G_loss_record.append(G_loss_val)
        
        print('Epoch:', '%04d' % epoch, 'D_loss: {:.4}'.format(D_loss_val), 'G_loss: {:.4}'.format(G_loss_val))

        plt.figure(figsize = (5,5))
        noise = make_noise(1, n_G_input)
        _, train_y = mnist.train.next_batch(1)
        G_img = sess.run(G_output, feed_dict = {z: noise, c: train_y})   
        plt.imshow(G_img.reshape(28,28), 'gray')
        plt.axis('off')
        plt.show()

Epoch: 0000 D_loss: 1.366 G_loss: 0.7145

Epoch: 5000 D_loss: 0.3833 G_loss: 2.581

Epoch: 10000 D_loss: 0.3294 G_loss: 2.688

Epoch: 15000 D_loss: 0.3761 G_loss: 2.796

Epoch: 20000 D_loss: 0.5413 G_loss: 2.56

Epoch: 25000 D_loss: 0.5124 G_loss: 2.364

Epoch: 30000 D_loss: 0.6452 G_loss: 2.295

Epoch: 35000 D_loss: 0.7431 G_loss: 1.939

Epoch: 40000 D_loss: 0.7072 G_loss: 1.916

Epoch: 45000 D_loss: 0.8109 G_loss: 1.606

Generate fake MNIST images by CGAN

noise = make_noise(1, n_G_input)
G_img = sess.run(G_output, feed_dict = {z: noise, c: [[0,0,0,0,0,1,0,0,0,0]]})

plt.figure(figsize = (5,5))
plt.imshow(G_img.reshape(28,28), 'gray')
plt.axis('off')
plt.show()

6. Other Tutorials

• Ian Goodfellow, et al., "Generative Adversarial Nets" NIPS, 2014.

• At NIPS 2016 by Ian Goodfellow

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• CS231n: CNN for Visual Recognition
  • Lecture 13: Generative Models
  • By Prof. Fei-Fei Li at Stanford University
  • http://cs231n.stanford.edu/

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MIT by Aaron Courville

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Univ. of Wateloo By Ali Ghodsi

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• 1시간만에 GAN (Generative Adversarial Network) 완전 정복하기
  • by 최윤제 (고려대 석사생)
  • YouTube: https://www.youtube.com/watch?v=odpjk7_tGY0
  • Slides: https://www.slideshare.net/NaverEngineering/1-gangenerative-adversarial-network

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<center><iframe src="https://www.youtube.com/embed/odpjk7_tGY0?rel=0" 
width="560" height="315" frameborder="0" allowfullscreen></iframe></center>

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